PROBLEM 2E

Let P(A) = 0.3 and P(B) = 0.6.

(a) Find P(A ∪ B) when A and B are independent.

(b) Find P(A|B) when A and B are mutually exclusive.

Solution 2E

Step1 of 3:

We have,

P(A) = 0.3 and

P(B) = 0.6

We need to find,

a).P(AB) when A and B are independent.

b).P(A/B) when A and B are mutually Exclusive.

Step2 of 3:

a).

P(AB) can be calculated by using the formula P(AB) = P(A) + P(B) - P(AB)

Where,

P(AB) = P(A)P(B) [because we know that A and B are independent]

= 0.30.6

= 0.18

Hence,P(AB) = 0.18.

Now,

P(AB) = P(A) + P(B) - P(AB)

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